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Question

1) How far will a wheel with a radius of 35 inches travel in one turn? 


2)Find the volume of a cylinder whose base has a diameter of 14 feet and whose height is 23 feet. 


3)Find the volume of a sphere with a radius of 15 yards. 


4)Find the volume of a cone with a radius of 22 millimeters and height of 24 millimeters. 



 

Answer 1

1).

Radius of a wheel (r) = 35 in.

Number of revolutions = 1.

Distance = circumference * no of revolutions

                = 2πr  * 1

Substitute the values of π = 3.14 and r = 35 in 2πr  * 1

Distance = 2 * 3.14 * 35 * 1

= 70 * 3.14

= 219.8 in.

2).

Diameter of a cylinder (d) = 2r = 14 ft ⇒ r = 14/2 = 7 ft.

Height (h) = 23 ft.

Volume of the cylinder (V) = πr²h.

Substitute the values of r = 7, h = 23, and π = 3.14 in V = πr²h.

V = 3.14 * (7)² * 23

= 3538.78 ft³ .

Volume of the cylinder is 3538.78 ft³ .

3).

Radius of the sphere (r) = 15 yd.

Volume of the sphere (V) = 4/3(πr³).

Substitute the values of r = 15 and π = 3.14 in V = 4/3(πr³).

V = 4/3(3.14 * 15³)

= 14130 yd³ .

Volume of the sphere is 14130 yd³.

4).

Radius of the cone (r) = 22 mm.

Height (h) = 24 mm.

Volume of a cone (V) = 1/3(πr²h).

Substitute the values of r = 22, h = 24, and π = 3.14 in V = 1/3(πr²h).

V = 1/3(3.14 * 22² * 24)

= 36474.24/3

= 12158.08.

Volume of the ice cream cone is 12158.08 mm³ .